On the geometric invariant theory of infinite groups generated by skew reflections (Q1580394)

In the real Euclidean space \(E^m\), we define an \((m-1)\)-dimensional noncylindrical surface \(F_n\) of order \(n\) that is invariant with respect to the infinite group \(G_\mu\) generated by skew (in particular, orthogonal) reflections relative to \((m-1)\)-dimensional planes which form the set \(B_\mu\). The symmetry directions of the planes of \(B_\mu\) are defined by vectors and compose the set \(N_\mu\); the \(\mu\)-plane \(\prod^\mu\) is its linear span. If the superscript \(c\) \((s\) or \(t)\) is written in the symbols \(B_\mu\), \(N_\mu\), \(\prod^\mu\) and \(G_\mu\), then this means that symmetry directions are nonasymptotic (asymptotic) for the surface \(F_n\); \(s\) and \(t\) correspond to different types of asymptotic directions. The geometrical invariant theory of the groups \(G_\mu\) was considered in earlier papers of the same author. In this paper previous results and also given new results of the same theory are mentioned.